Properties

Base field 5.5.157457.1
Label 5.5.157457.1-27.1-d
Conductor 27.1
Rank \( 1 \)

Related objects

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Base field 5.5.157457.1

Generator \(a\), with minimal polynomial \( x^{5} - 2 x^{4} - 4 x^{3} + 5 x^{2} + 4 x - 1 \); class number \(1\).

Elliptic curves in class 27.1-d over 5.5.157457.1

Isogeny class 27.1-d contains only one elliptic curve.

Curve label Weierstrass Coefficients
27.1-d1 \( \bigl[a^{2} - 2\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 3 a + 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( 2 a^{4} - 6 a^{3} - 4 a^{2} + 15 a + 1\) , \( 0\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph